The long-term aim of this project is the improvement of tomographic imaging in diagnostic radiology and nuclear medicine, especially positron emission tomography (PET). The project involves computer methods for generating images from the raw detector measurements of PET scanners (i.e., algorithms for image reconstruction from projection data). Data-driven methods that process each individual measurement in its original form (i.e., list-mode data) can extract more information from the data, compared to the more common methods that process data that are accumulated in histogram bins in the measurement space. For list-mode data, the reconstruction algorithms available at present consist of operations that are basically ' the same as those for binned data. However, the methods and feasibility studies in this exploratory/developmental proposal involve a conceptually different view of reconstruction from list-mode data that leads to alternative operations, specifically tailored to list-mode data, within both iterative and non-iterative algorithms. These operations are based on smooth localized kernels (e.g., Gaussians) in the measurement space, where each kernel extends over a limited region in both the linear and angular parameters. The operations involve backprojection of the kernel (or of a filtered kernel) into the image space, and the corresponding forward projection from the image space into the kernel's region of the measurement space. The project aims to develop, implement, test, and evaluate for feasibility both iterative and non-iterative algorithms using the new kernel-based operations for image reconstruction from list-mode data. Cancer imaging with PET, especially whole-body scanning, is limited by the low numbers of counts obtainable in the emission and transmission data sets. Improving the quantitative accuracy and signal-to-noise performance of clinically practical data acquisition and processing in PET would lead to improved detection, diagnosis, and treatment planning of cancer.